Angle dependence of the ferromagnetic resonance linewidth in easy-axis and easy-plane single crystal hexagonal ferrite disks

Ferromagnetic resonance measurements were made as a function of the static external field angle for $c$ -plane disks of single crystal flux grown manganese substituted barium $M$ -type (Ba-$M$ ) and zinc $Y$ -type (Zn-$Y$ ) hexagonal ferrites at 50 and 8.8 GHz, respectively. A shorted waveguide technique was used. Analysis of the FMR field versus angle results confirmed the operational assumption of a uniform mode response. For the easy-axis Ba-$M$ disk, the linewidth was 69 Oe when the external field and magnetization vectors were perpendicular to the disk. The linewidth increased to a maximum measured value of 472 Oe when the magnetization was directed 45.4° from the sample normal. For the easy-plane Zn-$Y$ disk, the linewidth had a minimum value of 18 Oe when the field and magnetization vectors were in-plane. The maximum linewidth was 391 Oe when the magnetization was directed 25.2° from the disk normal. The linewidths were larger than predicted for reasonable values of the Landau–Lifshitz damping and showed angle dependences which indicated nonintrinsic contributions to the loss. A modified two magnon scattering calculation based on the model of Sparks, Loudon, and Kittel was used to investigate these linewidth differences. The calculation included anisotropy modifications to the spin wave band for each material. The angle dependences of the excess linewidths show qualitative agreement with the two magnon predictions, with inhomogeneity sizes on the order of 1 and 0.25 μm and volume fractions of 0.01 and 0.005 for the Ba-$M$ and Zn-$Y$ disks, respectively.